Self-Organization in a Granular Medium by Internal Avalanches

Internal avalanches of grain displacements can be created inside a granular material kept in a bin in two ways: (i) by removing a randomly selected grain at the bottom of the bin; and (ii) by breaking a stable arch of grains clogging a hole at the bottom of the bin. Repeated generation of such avalanches leads the system to a steady state. It is relevant to ask whether this state is a critical state, as in self-organized criticality (SOC). We review here some recent studies of this problem using cellular automata and hard-disc models.     

A Straightforward $hp$-Adaptivity Strategy for Shock-Capturing with High-Order Discontinuous Galerkin Methods

In this paper, high-order Discontinuous Galerkin (DG) method is used to solve the two-dimensional Euler equations. A shock-capturing method based on the artificial viscosity technique is employed to handle physical discontinuities. Numerical tests show that the shocks can be captured within one element even on very coarse grids. The thickness of the shocks is dominated by the local mesh size and the local order of the basis functions. In order to obtain better shock resolution, a straightforward $hp$-adaptivity strategy is introduced, which is based on the high-order contribution calculated using hierarchical basis. Numerical results indicate that the $hp$-adaptivity method is easy to implement and better shock resolution can be obtained with smaller local mesh size and higher local order.     

A Front-Tracking Method for Motion by Mean Curvature with Surfactant

In this paper, we present a finite difference method to track a network of curves whose motion is determined by mean curvature. To study the effect of inhomogeneous surface tension on the evolution of the network of curves, we include surfactant which can diffuse along the curves. The governing equations consist of one parabolic equation for the curve motion coupled with a convection-diffusion equation for the surfactant concentration along each curve. Our numerical method is based on a direct discretization of the governing equations which conserves the total surfactant mass in the curve network. Numerical experiments are carried out to examine the effects of inhomogeneous surface tension on the motion of the network, including the von Neumann law for cell growth in two space dimensions.     

Avalanches and scaling in plastic deformation

Plastic deformation of crystalline materials is a complex nonhomogeneous process characterized by avalanches in the motion of dislocations. We study the evolution of dislocation loops using an analytically solvable phase-field model of dislocations for ductile single crystals during monotonic loading. The distribution of dislocation loop sizes is given by P(A) approximately A-sigma, with sigma=1.8+/-0.1. The exponent is in agreement with those found in acoustic emission experiments. This model also predicts a range of macroscopic behaviors in agreement with observation, including hardening with monotonic loading, and a maximum in the acoustic emission signal at the onset of yielding.     

Nowcasting Avalanches as Earthquakes and the Predictability of Strong Avalanches in the Olami-Feder-Christensen Model

Nowcasting earthquakes, suggested recently as a method to estimate the state of a fault and hence the seismic risk, is based on the concept of natural time. Here, we generalize nowcasting to a prediction method the merits of which are evaluated by means of the receiver operating characteristics. This new prediction method is applied to a simple (toy) model for the waiting (natural) time of the stronger earthquakes, real seismicity, and the Olami-Feder-Christensen earthquake model with interesting results revealing acceptable to excellent or even outstanding performance.     

Avalanches and Self-Organized Criticality in superconductors

We review the use of superconductors as a playground for the experimental study of front roughening and avalanches. Using the magneto-optical technique, the spatial distribution of the vortex density in the sample is monitored as a function of time. The roughness and growth exponents corresponding to the vortex `landscape' are determined and compared to the exponents that characterize the avalanches in the framework of Self-Organized Criticality. For those situations where a thermo-magnetic instability arises, an analytical non-linear and non-local model is discussed, which is found to be consistent to great detail with the experimental results. On anisotropic substrates, the anisotropy regularizes the avalanches.     

Kinetic Models for Granular Flow

The generalization of the Boltzmann and Enskog kinetic equations to allow inelastic collisions provides a basis for studies of granular media at a fundamental level. For elastic collisions the significant technical challenges presented in solving these equations have been circumvented by the use of corresponding model kinetic equations. The objective here is to discuss the formulation of model kinetic equations for the case of inelastic collisions. To illustrate the qualitative changes resulting from inelastic collisions the dynamics of a heavy particle in a gas of much lighter particles is considered first. The Boltzmann–Lorentz equation is reduced to a Fokker–Planck equation and its exact solution is obtained. Qualitative differences from the elastic case arise primarily from the cooling of the surrounding gas. The excitations, or physical spectrum, are no longer determined simply from the Fokker–Planck operator, but rather from a related operator incorporating the cooling effects. Nevertheless, it is shown that a diffusion mode dominates for long times just as in the elastic case. From the spectral analysis of the Fokker–Planck equation an associated kinetic model is obtained. In appropriate dimensionless variables it has the same form as the BGK kinetic model for elastic collisions, known to be an accurate representation of the Fokker–Planck equation. On the basis of these considerations, a kinetic model for the Boltzmann equation is derived. The exact solution for states near the homogeneous cooling state is obtained and the transport properties are discussed, including the relaxation toward hydrodynamics. As a second application of this model, it is shown that the exact solution for uniform shear flow arbitrarily far from equilibrium can be obtained from the corresponding known solution for elastic collisions. Finally, the kinetic model for the dense fluid Enskog equation is described.     

Avalanches in a nonlinear oscillator chain in a periodic potential

We consider the dynamics of a chain of coupled units evolving in a periodic substrate potential. The chain is initially in a flat state and situated in a potential well. A bias force, acting as a weak driving mechanism, is applied at a single unit of the chain. We study the instigation of directed transport in two types of system: (i) a microcanonical situation associated with deterministic and conservative dynamics and (ii) the Langevin dynamics when the system is in contact with a heat bath. Interestingly, for the deterministic and conservative dynamics the directed transport is drastically enhanced compared with its Langevin counterpart. In particular, in the deterministic and conservative regime a self-organised redistribution of energy triggers huge-sized avalanches yielding ultimately accelerated transport of the chain. In contrast, in the thermally-assisted process between avalanches the chain settles always into a pinned metastable state impeding continual accelerated chain motion.     

Superfluid Avalanches in Nuclepore: Constrained versus Free-Boundary Experiments and Simulations

Superfluid 4He exhibits hysteretic behavior in the percolated nanoporous material Nuclepore during the filling and draining of pores due to capillary condensation, and one observes avalanches during the pore draining. We observe that the size and frequency of the avalanches depend upon whether the fluid flow off the substrate during draining is impeded or unimpeded. We simulate the draining of superfluid 4He from Nuclepore with and without a perturbation of the pore menisci and find results similar to the results seen in the experiments in the presence or the absence of flow inhibition.     

碳质球粒陨石和普通球粒陨石的拉曼光谱

碳质球粒陨石和普通球粒陨石的拉曼光谱陈建，张卫红，张卓良（中山大学测试中心广州５１０２７５）李肇辉，王瑛（中科院广州地质新技术研究所广州５１０６４０）ＲａｍａｎｓｐｅｃｔｒｏｓｃｏｐｙｏｆＣａｆｂｏｎａｃｅｏｕｓＧｒａｎｕｌａｒＡｅｒｏｌｉｔｅａｎｄ...     

Granular ratchets

We study the statistics of the horizontal component of atmospheric boundary layer wind speed and introduce a stochastic process which has similar properties. Motivated by the non-stationarity of wind velocity data, we describe statistical methods to verify the picture of natural atmospheric boundary layer turbulence to be composed of successively occurring close to ideal turbulence phases with different parameters. We focus on the fluctuation of wind speed around its mean behaviour and show that there is linear relationship between the standard deviation of the fluctuation and the current mean wind speed. Additionally, we analyse the increment statistics and investigate the time dependence of the parameters describing the increment distribution. Noting that the first order geometric auto regressive process has similar statistical properties, we investigate this similarity and analyse the extent to which this stochastic process is a suitable model for wind speed simulation.     

Granular packings and fault zones

The failure of a two-dimensional packing of elastic grains is analyzed using a numerical model. The packing fails through formation of shear bands or faults. During failure there is a separation of the system into two grain-packing states. In a shear band, local "rotating bearings" are spontaneously formed. The bearing state is favored in a shear band because it has a low stiffness against shearing. The "seismic activity" distribution in the packing has the same characteristics as that of the earthquake distribution in tectonic faults. The directions of the principal stresses in a bearing are reminiscent of those found at the San Andreas Fault.